Complex numbers worksheet with answers

Free printable Complex numbers worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
ReIm55−5−5z₁z₂

For z₁ = −2 + j8 and z₂ = 2 − j4, find the imaginary part of w = 2z₁ + 2z̄₂.

z₁ = −2 + j8z₂ = 2 − j4
Im(w) =
2.Easy
ReIm55−5−5z₁z₂

For z₁ = −7 − j2 and z₂ = 6 − j, find the real part of w = 2z₁ − 2z̄₂.

z₁ = −7 − j2z₂ = 6 − j
Re(w) =
3.Medium
ReIm55−5−5z₁z₂w

Given z₁ = 3∠125° and z₂ = 3∠80°, find the imaginary part of w = z₁·z₂.

z₁ = 3∠125°z₂ = 3∠80°
Im(w) =
4.Medium
ReIm55−5−5θz

Write z = 8∠160° in rectangular form a + jb and give the imaginary part b.

r = 8θ = 160°
b =
5.Hard
ReIm11−1−122−2−233−3−3z₀z₁z₂z₃

The roots of zⁿ = w with n = 4 and w = 81∠60° are zk = R1/n∠((φ + 360°·k)/n), k = 0, 1, 2, 3. Find the imaginary part of z₂.

w = 81∠60°n = 4k = 2
Im(z₂) =
6.Hard
ReIm11−1−122−2−2ABCD

Exactly one of the points A–D is a root of z³ = 8∠90°. Click it.

w = 8∠90°n = 3
  1. 1A (2∠90°)
  2. 2B (1∠150°)
  3. 3C (2∠−150°)
  4. 4D (2∠150°)

Answer key

  1. 1. Im(w) = 24
  2. 2. Re(w) = −26
  3. 3. Im(w) = −3.804
  4. 4. b = 2.736
  5. 5. Im(z₂) = −0.7765
  6. 6. D (2∠150°)

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